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RALEIGH, N.C. (AP) -- Dozens of volunteers armed with clipboards and voter registration forms gather at President Barack Obama’s field office here every day. Their mission: Fan out across the city seeking new voters in this rapidly growing state.

“Are you registered to vote at your current address?” asks Douglas Johnston, a volunteer wooing voters outside the county courthouse. “Do you know about early voting?”

The effort, it seems, has borne fruit—to the tune of more than 250,000 new registered voters in North Carolina since April 2011, according to Obama’s team. That’s more new voters than the campaign has registered anywhere else in the country.

It’s an eye-popping total in a state that Obama won by just 14,000 votes four years ago. And the flood of new voters—presumably a chunk of them Democrats—could help keep North Carolina within the president’s reach in a year when everything else here seems to be working in Republican Mitt Romney’s favor.

North Carolina has voted for a Democratic presidential candidate just twice in 40 years. The state’s economy is abysmal; its 9.7 percent unemployment rate is among the nation’s highest. And the president’s embrace of gay marriage put him at odds with a majority of North Carolina voters, including many blacks, who make up the core of his support here.

But less than six weeks from Election Day, Romney is spending millions of dollars in television advertising in North Carolina, defending territory that remains more conservative than most of the states that will decide the election. That raises questions about his chances in places like Ohio, Florida and Virginia, where polls show him trailing the president.

Compared with Obama, Romney has fewer paths to victory in the state-by-state contest to cobble together enough wins to reach the requisite 270 Electoral College votes. That makes North Carolina’s 15 electoral votes more important to him than to Obama, who could still win the White House without a North Carolina victory.

Romney’s campaign won’t say how many new voters they have registered in the state.

And registration numbers alone don’t tell the whole story in North Carolina. Democrats have long outnumbered Republicans in the state, even though voters sided with GOP presidential candidates for decades. And Democratic registration has fallen by about 90,000 since the end of 2008, while unaffiliated voters have increased by more than 250,000.

A shortage of independent polls in North Carolina makes the state’s status 40 days out hard to judge. An NBC News/Wall Street Journal/Marist Poll out Thursday showed Obama leading Romney among likely voters 48 percent to 46 percent.

But both parties say the race is tight.

“Changing demographics have made this state more competitive than past years,” said Robert Reid, Romney’s North Carolina communications director. But he expressed confidence that the lagging economy would help the Republican win a close contest.

“The race is, and has been, within the margin of error,” said Ken Eudy, a veteran Democratic strategist in North Carolina.

North Carolina’s rapid transition from a GOP stalwart to a presidential battleground has largely been due to increased voter registration of new African-American and Hispanic residents, as well as of transplants from the Northeast.

They’re people like Diana Hrabosky, a Democrat who just moved to the state and registered to vote on Wednesday with an Obama campaign volunteer. And Walter Woody III, who recently turned 18 and is eligible to vote for the first time.

“It seems like no matter what race you are, people are starting to get more Democratic,” said Woody, who is black, after he finished filling out a registration form.

This year, Romney’s campaign was determined not to get caught off guard in North Carolina like GOP nominee John McCain was four years ago. Republicans have built a more substantial ground operation here, but still trail Obama in manpower. The president has 53 field offices across North Carolina to Romney’s 24.

About 1.6 million people in North Carolina, or one-fourth of the electorate, are registered to vote but not affiliated with a party.

Paul Shumaker, a Republican consultant who has handled statewide races, said those voters may present just as many problems for Romney as the Democrats.

“Having to go through a Republican primary that pulled him to the right hurts him in building a winning coalition in the state,” Shumaker said.

Theresa Jeffers is one of the unaffiliated voters siding with Romney—though she says it’s more a vote against Obama than in favor of the Republican.

“I was hoping so much that he would be successful,” Jeffers, 64, said of the president. She said she’s been disappointed by his performance in office, particularly on the debt.

Romney is hoping millions of dollars in television advertisements will convince more voters like Jeffers to side with him. The candidate and his GOP allies have spent more than $32 million on ads in North Carolina, including $2 million last week alone.

Obama and Democrats have spent nearly $18 million on North Carolina advertising. But their rate of weekly spending has slowed, down about half from their peak in the summer. Obama’s campaign is also not running the costly two-minute ad it released Thursday in the state.

Neither candidate has devoted much time on the ground in North Carolina. Romney has made four trips to the state, while Obama has been here three times, including during the Democratic Party’s convention in Charlotte earlier this month. But their running mates and wives have been frequent visitors.

Obama had planned to deliver his acceptance speech at a Charlotte football stadium with seating for 74,000 and use the gathering for voter registration and recruitment. But the outdoor event was canceled, with Democrats blaming the weather and Republicans accusing the president of not being able to draw a capacity crowd.